The present invention relates to the field of communications and more particularly to communications systems including equalizers used to detect coherent symbols and related methods.
In current D-AMPS (IS-136) cellular communications systems, maximum likelihood sequence estimation (MLSE) equalizers detect coherent symbol values using forward or backward detection at the mobile terminal depending on the quality of the current and next slot synchronization words. At the base-station, backward MLSE detection used for symbols to the left of the synchronization sequence and forward detection is used for symbols to the right of the synchronization sequence. For example, MLSE equalization in the forward direction can be performed using the Viterbi algorithm as discussed in the reference by Ungerboeck entitled xe2x80x9cAdaptive Maximum-Likelihood Receiver for Carrier-Modulated Data-Transmission Systemsxe2x80x9d, IEEE Trans. Comm., COM-22: pages 624-636, May 1974. The disclosure of this reference is hereby incorporated herein in its entirety by reference.
Overall log-likelihoods used to detect a sequence of symbols [a0, a1, . . . , aN] can take the form:                               l          ⁢                      {                          a              ;              y                        }                          =                              ∑                          n              =              0                        N                    ⁢                      xe2x80x83                    ⁢                                    [                                                2                  ⁢                  ℜ                  ⁢                                      {                                                                  a                        n                        *                                            ⁢                                              z                        n                                                              }                                                  -                                                                            "LeftBracketingBar"                                              a                        n                                            "RightBracketingBar"                                        2                                    ⁢                                      s                                          0                      ,                      n                                                                      -                                                      ∑                                          l                      -                      1                                                              min                      ⁡                                              (                                                  n                          ,                          N                                                )                                                                              ⁢                                      xe2x80x83                                    ⁢                                      2                    ⁢                    ℜ                    ⁢                                          {                                                                        a                          n                          *                                                ⁢                                                  s                                                      l                            ,                            n                                                                          ⁢                                                  a                                                      n                            -                            1                                                                                              }                                                                                  ]                        .                                              (        1        )            
In this equation, the equalization parameters zn and sl,n are described in the Ungerboeck reference, and these equalization parameters are extended to fractionally-spaced receivers in the reference by Molnar et al. entitled xe2x80x9cA Novel Fractionally-Spaced MLSE Receiver And Channel Tracking With Side Informationxe2x80x9d, Proc. 48th IEEE Veh. Tech. Conf., May 1998. The disclosure of this reference is hereby incorporated herein in its entirety by reference.
The term inside the square brackets of Equation (1) forms the metric for the symbol an. This approach takes advantage of the symmetry of the sl,n terms, and the summation of the s-terms is shown in FIG. 1 for an example with N=2. The circles correspond to the s0,n terms and for each n, the s-terms to the left and to the top of the circled s0,n terms correspond to the terms sl,n for a specific value of n.
When backward equalization is used, the following log-likelihood is used to determine the metric for the Viterbi algorithm:                                           l            ⁢                          {                              a                ;                y                            }                                =                                    ∑                              n                =                0                            N                        ⁢                          xe2x80x83                        ⁢                          [                                                2                  ⁢                  ℜ                  ⁢                                      {                                                                  a                        n                        *                                            ⁢                                              z                        n                                                              }                                                  -                                                                            "LeftBracketingBar"                                              a                        n                                            "RightBracketingBar"                                        2                                    ⁢                                      s                                          0                      ,                      n                                                                      -                                                      ∑                                          l                      =                      1                                                              min                      ⁡                                              (                                                                              N                            -                            n                                                    ,                          N                                                )                                                                              ⁢                                      xe2x80x83                                    ⁢                                      2                    ⁢                    ℜ                    ⁢                                          {                                                                        a                          n                          *                                                ⁢                                                  s                                                      l                            ,                                                          n                              +                              l                                                                                *                                                ⁢                                                  a                                                      n                            +                            l                                                                                              }                                                                                  ]                                      ⁢                  xe2x80x83                                    (        2        )            
Note that the first two terms in the metric are the same for either forward or backward equalization, while the summation of the s-terms is different. The summation of the s-terms for this case is shown in FIG. 2, again for the case of N=2. The circled terms remain the same as for the forward metric, but now the s-terms for a specific value of n are chosen as those terms to the right and below the n""th diagonal element.
For differential-QPSK modulation, the coherent symbols can be estimated using the above MLSE equalization approach. Estimates of the differential symbols and bits can then be obtained from the detected coherent symbols, while soft differential bit information can be obtained from the saved equalization metrics as discussed in the reference by Bottomley entitled xe2x80x9cSoft Information in ADCxe2x80x9d, Technical Report, Ericsson-GE, 1993. The disclosure of this reference is hereby incorporated herein in its entirety by reference.
For digital communications, maximum a-posterori (MAP) detection has been used as discussed in the reference by Bahl et al. entitled xe2x80x9cOptimal Decoding of Linear Codes for Minimizing Symbol Error Ratexe2x80x9d, IEEE Trans. Inf. Theory, IT-20: pages 284-287, March 1974. This approach is also similar to approaches discussed in the following references: Baum et al., xe2x80x9cA Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chainsxe2x80x9d, Ann. Math. Statist., 41: pages 164-171, 1970; Sundberg, xe2x80x9cAn Iterative Method for Solution of the Likelihood Equations for Incomplete Data from Exponential Familiesxe2x80x9d, Comm. Statist. Simulation. Comput., B5: pages 55-64, 1976; Erkurt et al., xe2x80x9cJoint Detection and Channel Estimation for Rapidly Fading Channelsxe2x80x9d, Globecom 1992, pages 910-914, December 1992; Kaleh et al., xe2x80x9cJoint Parameter Estimation and Symbol Detection for Linear or Nonlinear Unknown Channelsxe2x80x9d, IEEE Trans. Comm. 42(7): pages 2406-2413, July 1994; Krishnamurthy, xe2x80x9cAdaptive Estimation of Hidden Nearly Completely Decomposable Markov Chains With Applications in Blind Equalizationxe2x80x9d, xe2x80x9cInternational Journal of Adaptive Control and Signal Processingxe2x80x9d, 8: pages 237-260,1994; Cirpan et al., xe2x80x9cStochastic Maximum Likelihood Methods for Semi-Blind Channel Estimationxe2x80x9d, IEEE Signal Processing Letters, 5(1): pages 21-24, January 1998; and Baccarelli et al., xe2x80x9cCombined Channel Fast-Fading Digital Linksxe2x80x9d, IEEE Trans. Comm., 46(4): pages 424-427, April 1998. The disclosures of each of these references are hereby incorporated herein in their entirety by reference.
The metric for MAP detection of the coherent symbols can be derived from the following overall log-likelihood:                               l          ⁢                      {                          a              ;              y                        }                          =                                            ∑                              n                =                0                            N                        ⁢                          xe2x80x83                        ⁢                          2              ⁢              ℜ              ⁢                              {                                                      a                    n                    *                                    ⁢                                      z                    n                                                  }                                              -                                    ∑                              n                =                0                            N                        ⁢                          xe2x80x83                        ⁢                                          ∑                                  m                  =                  0                                N                            ⁢                              xe2x80x83                            ⁢                                                a                  n                  *                                ⁢                                  h                                      n                    ,                    m                                                  ⁢                                                      a                    m                                    .                                                                                        (        3        )            
The MAP metric is found by collecting all terms containing an. For example, in FIG. 3A, the symbol a1 contribution to the double sum in Equation (3) is shown by the enclosed hn,m terms. The hn,m terms are related to the s-parameters in the following manner:                               h                      n            ,            m                          =                  {                                                                      s                                                            n                      -                      m                                        ,                    n                                                                                                                    n                    ≥                    m                                    ;                                                                                                                          s                                                                  n                        -                        m                                            ,                      m                                                        =                                      s                                                                  m                        -                        n                                            ,                      m                                        *                                                                                                n                   less than                                       m                    .                                                                                                          (        4        )            
The corresponding terms are shown in FIG. 3B. Using the s-parameters from FIG. 3B, the contribution to the MAP metric for symbol an can be written as:                               l          ⁢                      {                                          a                n                            ;              y                        }                          =                              2            ⁢            ℜ            ⁢                          {                                                a                  n                  *                                ⁢                                  z                  n                                            }                                -                                                    "LeftBracketingBar"                                  a                  n                                "RightBracketingBar"                            2                        ⁢                          s                              0                ,                n                                              -                                    ∑                              l                =                1                                            min                ⁡                                  (                                      n                    ,                    N                                    )                                                      ⁢                          xe2x80x83                        ⁢                          2              ⁢              ℜ              ⁢                              {                                                      a                    n                    *                                    ⁢                                      s                                          l                      ,                      n                                                        ⁢                                      a                                          n                      -                      l                                                                      }                                              -                                    ∑                              l                =                1                                            min                ⁡                                  (                                                            N                      -                      n                                        ,                    N                                    )                                                      ⁢                          xe2x80x83                        ⁢                          2              ⁢              ℜ              ⁢                              xe2x80x83                            ⁢              y              ⁢                                                {                                                            a                      n                      *                                        ⁢                                          s                                              l                        ,                        n                                            *                                        ⁢                                          a                                              n                        +                        l                                                                              }                                .                                                                        (        5        )            
The terms contributing to the double summation in Equation (3) use the same folding as in the forward and backward MLSE equalizers previously discussed.
Notwithstanding the equalizer systems and methods discussed above, there continues to exist a need in the art for improved equalizer systems and methods.
It is therefore an object of the present invention to provide improved methods and receivers for receiving data transmitted over radio communications channels.
This and other objects are provided according to the present invention by methods for receiving data transmitted over a radio communications channel wherein the data is transmitted as a plurality of sequential symbols wherein each sequential symbol is determined as a function of a previous symbol and a respective differential symbol corresponding to a portion of the data being transmitted. A plurality of received segments are sampled wherein the received segments correspond to respective ones of the transmitted symbols, and an initial differential MAP symbol estimation is performed for estimated received symbols corresponding to the sampled received segments to provide initial estimates of the differential symbols. New received symbol estimates are calculated using the initial estimates of the differential symbols, and a subsequent differential MAP symbol estimation is performed using the new received symbol estimates to provide improved estimates of the differential symbols. Bit probability calculations are performed on the improved estimates of the differential symbols. Improved data reception can thus be provided over radio communications channels.
The steps of calculating the new received symbol estimates and performing subsequent differential MAP symbol estimation can be repeated at least once and the bit probability calculations can be performed on the improved estimates of the differential symbols provided during subsequent differential MAP symbol estimation. More particularly, the steps of calculating the new received symbol estimates and performing subsequent differential MAP symbol estimation can be repeated a predetermined number of times. Alternately, the steps of calculating the new received symbol estimates and performing subsequent differential MAP symbol estimation can be repeated until the improved estimates of the differential symbols converge to within a predetermined threshold.
In addition, the estimates of the bit values can be decoded. Furthermore, the decoded estimates of the bit values can be re-encoded to provide re-encoded received symbol estimates, subsequent differential MAP symbol estimation can be performed using the re-encoded received symbol estimates to provide further improved estimates of the differential symbols, and bit probability calculations can be performed on the further improved estimates of the differential symbols.
The steps of performing the differential MAP symbol estimation can each comprise performing log-likelihood calculations for estimated received symbols corresponding to the sampled transmission segments, and performing differential symbol probability calculations. The log-likelihood calculations can also be preceded by estimating channel parameters based on the sampled transmission segments wherein the log-likelihood calculations use the estimated channel parameters. More particularly, the estimated channel parameters can be estimated s-parameters and z-parameters.
The methods and receivers of the present invention can thus provide improved data reception.